Yeah, it's self-aware in that they know what they're making, because they're human beings. And consciously choose to make that thing instead of including ironic detachment in the script.
I could also just list the jokes that are
in the series about characters not understanding their own story, but I won't go to the effort, but they're there
Except all those examples are...completely the opposite.
That doesn't matter? This is how people treat JP game stories in general, of course all of them are totally different than eachother in reality. But every single one I have seen get hit with "the director doesn't know what they're doing and made all of this on accident" at some point or another. Kojima understanding storytelling and characterization is often a pretty controversial statement, even if it's obvious to you and me that he does. (Also killer7 is not so difficult to describe exactly what it's doing IMO.)
KH is built the way it is for a reason too, but again I don't know if I should go to the effort of explaining it, we're already on a Kingdom Hearts forum... if it all seems like a joke to you and you are caught up, that won't change.
I will give you one recent example (of many) of Kingdom Hearts poking fun of itself, though: In Dark Road, the characters go to visit Hades to contact characters who have died, and they know
they've died. They still tell Hades they want to see people who have "disappeared". Hades is like, "What- oh. don't you mean 'dead'?" and Xehanort goes "Whatever." This is a clear joke about how KH tends to use euphamisms for "death" instead of saying the actual word, even when it actually applies.
Or see also the Organization expressing interest in Davy Jones' box in III, said to contain his heart. When they realize it's the actual organ, the heart, which the series has avoided mentioning until this point, they both understand the concept and react in annoyance that that's what they meant by "heart".
Actually, there's a lot of that kind of thing, the difference between the way "Kingdom Hearts characters" see the world and the way Disney characters see the world, since they come from a movie with its own rules that was never meant to operate in the KH universe. The series is aware of this contradiction that has existed since the first game, of course.